The opening of the Kiev Polytechnic Institute held August 31, 1898 KPI first director (1898-1902 biennium) was an outstanding scientist, talented teacher, a brilliant organizer of technical education professor. VL Kyrpychov. Deans of departments (faculties) are known and scientists. skilful organizers of the educational process Professors KO Zvorykin (mechanical and resident engineering faculties), NI Konovalov (Chemistry), M. Chyrvinskyy (Agronomy). To ensure the teaching of all subjects at the institute was established 35 departments.

During the selection of teachers for the institute focused on research activities, pedagogical skills, organizational skills of applicants, their ability to communicate with students. An example to follow prof.V.L.Kyrpychov was the first director of the Institute and Chair of resistance. The organization of educational process, he kept the progressive principles that lie in a combination of theoretical learning lab in the workshops and practical training at enterprises. VL Kyrpychov had the rare talent of teaching. His lectures were marked by simplicity and conviction, both clear and fun style of teaching. All heard vykarbovuvalosya long in the grateful memory of students.

From the first days of the Institute (1898) became increasingly important mathematical training in the technical education students.

The first Head of Department of Mathematics was a visiting professor, Corresponding Member of the Academy of Sciences VP Ermakov (1845-1922), who previously served as professor of Kiev University. He taught mathematics in engineering and mechanical departments of the Institute.

Creative interests VP Ermakova concerned primarily the theory of differential equations as ordinary and partial, and the theory of series, calculus of variations, theory of special functions, algebra and number theory. He also enriched the science of original research in theoretical mechanics .

From 1898 to 1922, VP Ermakov taught introduction to the analysis, higher algebra, analytical geometry, differential and integral calculus and introduced the first practical lessons in these subjects. Moreover, his lectures were studied and the subjects are not characteristic for the technical institutions of the time: the elements of differential geometry, theory of ordinary differential equations as well as partial elements of probability theory, composition empirical formula and approximate calculation. He also facilitated introduction of a small course on the study slide rule. His lectures were marked by theoretical depth utmost clarity, liveliness and simplicity of presentation. These same advantages were noted and his books on mathematics and mechanics. He believed that the training courses should interest students, not scare them. Therefore the study of mathematics is not restricted only to lectures, and introduced a large number of exercises that provided an opportunity for students to work independently on the solution of practical problems.

Name VP Ermakova became widely known in European science in relation to open it (in 1871) znakododatnyh sign of convergence of numerical series. It is also known as a prominent Methodist in higher and elementary mathematics, as well as the organizer of the 1884 edition of the Journal of elementary mathematics, which enjoyed great popularity, especially among teachers. By the end of his life remained a scientist on the labor of fasting, giving your strength training engineering personnel.

Closest aides, VP Ermakova BYa.Bukreyev was Professor (1859-1962), who mainly taught in the Faculty of Chemistry, and after death and Ermakova B.P to 1930 he was head of the department of mathematics. His master's and doctoral dissertations were devoted to the analytical theory of special functions. Thereafter, the subject of creative interests BJ Bukreyev was geometry, particularly non-Euclidean geometry.

Demonstrator were Belyankin II, II Panfilov, GV Pfeyfer, MO Stolyarov, P. Voronets, later SP Schoenberg, O.II.Korobov, PhD . Abramovich. Some of them subsequently became prominent scientists in mathematics and mechanics. Thus, P. Voronets became one of the founders of nonholonomic mechanics, and GV Pfeyferu are fundamental results in the theory of differential equations with partial derivatives.

After BJ Bukreyev mathematics department until 1938 was headed by Professor M. Kravchuk (1892-1942) - Academy of Sciences of Ukraine, a talented scientist who has received important results in algebra, number theory and mathematical analysis. Published over 180 research papers M. Kravchuk. Kravchuk polynomials, formulas Kravchuk. Kravchuk oscillator and is now a powerful tool for research. His works have been used to develop the world's first electronic computer.

From the 1992 International Scientific Conference held behalf Kravchuk based KPI, in which scientists worked from 1921 to 1938 May 20, 2003 opened a monument to Kravchuk in our university.

In the next three years - until the summer of 1941 - led by the Department of Mathematics Corresponding Member of Academy of Sciences of Ukraine, Professor J. D. Sokolov (1895-1969) - known scientist in the field of theoretical mechanics and mathematics, student academic DA Grave.

During WWII KPI was evacuated to Tashkent and merged with Central Asian Industrial Institute. During this period in the early postwar years (until 1952) team of mathematicians institute headed by Professor A. Smohorzhevskyy (1896-1969), known for his scholarly works on the theory of Green's functions and especially in the field of geometric constructions on non-Euclidean plane. In 50 and 60 years of XX century. He was the recognized head of the Kiev school geometry.

In the second half of 1940 in a KPI mathematical work the first seminar, organized and was captain of his professor. OS Smohorzhevskyy. The seminar lasted over 20 years to the death of its founder. The main topic was non-Euclidean geometry, with emphasis on geometric constructions.

In the spring of 1952 Department of Mathematics KPI was divided into two: the department of mathematical physics NP headed by prof. OS Smohorzhevskym and Department of Mathematics, headed by prof. VA Zmorovychem.

VA Zmorovych (1909-1994) worked at KPI since 1932 more than 50 years and was well-known specialist in the theory of analytic functions.

Since 1974 the Department merged the two under the title Department of Mathematics (Head prof.L.Ye.Dunduchenko). At the same time evolved the Department of Computational Mathematics (Head prof.V.I.Kulya).

Since 1976 the Department of Mathematics headed by Professor F. P. Yaremchuk range of research which was mainly Hydromechanics and methods of teaching mathematics.

New Department of Mathematics was quite numerous and consisted of more than one hundred teachers. Such numerous department and it was difficult to manage because at the beginning of 1982 the issue of its division. This was due to the need for more optimal organization and management of educational process and his approach to the needs of specific departments. In April 1982 a decree concerning the division of the Department of Mathematics KPI into three departments: the Department of Mathematics number 1. Department of Mathematics number 2, Department of Mathematics number 3.

Thus, since the 1982/83 school year teaching mathematics at KPI performed three departments of higher mathematics. Each gave a specific group of mathematics education faculties of the institute.

From 1982 to 1998 Department of Mathematics headed prof.F.T.Baranovskyy number 2 - well-known specialist in the field of differential equations with partial derivatives. His scientific works are devoted to research and formulation of the Cauchy problem and mixed problem with initial conditions and vydozminnymy Goursat vydozminnymy with boundary conditions for degenerate hyperbolic equations. According to the results of these studies published over 50 scientific and methodological works.

From October 1998 the head of the Department of Mathematics number 2 is the academician of Ukraine, Professor AM Samoilenko - founder of scientific school of multifrequency vibration theory and the theory of pulse systems that recognized the mathematical centers of the world, one of the leading specialists in the field of ordinary differential equations and the theory of nonlinear oscillations.

From 1988 AM Samoilenko is the Director of the Institute of Mathematics NAS of Ukraine. In 1978 he was elected a corresponding member and in 1995 - full member (academician) of the National Academy of Sciences of Ukraine.

AM Samoilenko - author of 400 scientific publications including 16 monographs and 10 textbooks. Most of his works translated in foreign languages and published abroad.

Research interests Samoilenko cover a wide range of complex mathematical problems and urgent. International recognition of his research confirms the generally in world literature of mathematical terms: Numerical-analytic method of AM Samoilenko, "Green-Samoilenko function and others. Published his book made fundamental contributions to mathematics and its teaching.

AM Samoilenko pays great attention to training highly qualified scientific personnel. Among his pupils - 17 doctors and 67 candidates of Sciences, successfully working in many mathematical centers in different countries. Professor AM Samoilenko teaching at NTU "KPI" and the Kyiv National Taras Shevchenko University. He and President of the Ukrainian Mathematical Society, member of the American Mathematical Society and several other foreign Mathematical Society.

AM Samoilenko awarded the Order of Friendship of Peoples (1984) and the Order of Merit of the third degree (2003), Diploma of Presidium of Supreme Soviet of Ukraine (1987), has won the State Prize of Ukraine in Science and Technology (1985, 1996), Republican Prize. Ostrovsky (1968) Awards Academy of Sciences of Ukraine. Krylova (1981) and Bogoliubov (1998). Prize of NAS of Ukraine. Lavrent'ev (2000). Honoured Scientist of Ukraine (1998).

Mathematical talent Anatoly Mikhailovich combined with great organizational skills, integrity and humanity. With these qualities he has authority and respect among scholars, teachers, and students.

In September 2000 the Department of Mathematics number 2 was renamed the department of differential equations.

Department of Differential Equations to date has comprised: 4 professors, 22 associate professors, 3 senior lecturers, 7 assistants. Among them: 1 academician of Ukraine, 4 doctors, 24 candidates of science.

Research Department issues directly related to the development of modern theoretical and applied problems of mathematics and mechanics. Faculty conduct research on such key areas: ordinary differential equations and differential equations in partial derivatives, function theory, functional analysis, probability theory, mathematical statistics and queuing theory, theory of topological groups, mathematical theory of elasticity and plastic fluid mechanics, gas and plasma; sonar, continuum mechanics, history and methods of teaching mathematics.

Significant results were obtained by the department of theory of differential equations and their applications. First of all scientific papers should be noted head of the Department of Differential Equations of academician of NAS of Ukraine, Professor Anatoly Mikhailovich A.M.Samoylenka.Naukovi interests cover a wide range of complex and urgent problems of qualitative theory of differential equations and nonlinear mechanics. The original and insightful research AM Samoilenko for explaining the behavior of integral curves on the invariant toroidal manifolds and compact and in their neighborhood, developing perturbation toroidal varieties, creating new and asymptotic methods of nonlinear mechanics, developing the theory of multifrequency oscillations make a great contribution to their resolution, along with basic research in this field Bogoliubov, YA Mitropolsky, A. Kolmogorov, VI Arnol'd and J. Moser and identify new areas of study.

On the international recognition of his scientific work universally testify in mathematical literature of the time: "function Green-Samoilenko, Numerical-analytical method Samoilenko. Published his monograph, together with pupils make fundamental contributions to the development of the theory of multifrequency oscillations, asymptotic methods, pulsed systems and numerical-analytical methods. Research AM.Samoylenka ensure the continuation and development of mathematical traditions of the world famous school founded by Bogolyubov.

Professor SD Borysenko is a specialist in qualitative theory of differential equations, stability theory, the theory of impulsive systems. Him a doctor thesis (1998), dedicated to solving the problem Chaplygina intehrosumarnyh equations and obtaining the conditions of stability, practical stability, attraction of solutions of systems of differential equations with nonregular right-hand side. Professor SD Borisenko coordinator of international programs in mathematics, which is carried NTU "KPI", University of Rome "La sapiens and the University of Salerno. Repeatedly lectured to the faculty of the University of Bologna, Naples University, Rome University and the University of Salerno. Together with Academician of NAS of Ukraine, professor and Samoilenko and Professor V. Yasinskyi received the title of laureate of All-Ukraine Foundation to promote the development of mathematics in Ukraine for the best monograph of 2001.

Main scientific interests doctor of physics and mathematics GP Pelyuha related to the theory of functional differential and differential-functional equations. Among the results of GP Pelyuha a number of those that are fundamental for the further development of the theory of these equations, namely: the base built a local theory of systems of nonlinear functional equations, a method of Poincare normal forms for the study of nonlinear nonautonomous differential equations, established the basic theory of systems linear difference equations with continuous argument and periodic coefficients and proposed a number of new problems for functional differential equations and their solvability conditions are obtained for some classes of such equations.

Proceedings Assoc. ME Mr.Smith on the investigation of the properties of singularly perturbed operators, including a pair of commutative properties singularly perturbed operators.

Phys. AV Volkov explores the convergence of the different structures of linear operators. Whose values are as trigonometric and algebraic polynomials.

Proceedings Assoc. IP Grabovoy on the investigation of control of dynamic systems in conflict and uncertainty. The results are widely used in various sectors of the economy.

Assoc. BI Dzyra uses asymptotic methods in the trajectories of differential equations in partial derivatives with discontinuous coefficients and right-hand sides, and apply the averaging method to some nonlinear systems. The focus is the study of vibrations with distributed parameters.

Assoc. VF Zrazhevskaya explores the boundary problem with free boundary, also engaged in the development and improvement of numerical methods for boundary value problems of mathematical physics arising in electrodynamics nonideal environments. These problems, in addition to scientific interest, practical importance.

Phys. TV Karnaukhova explores the symmetric vibration of thin-walled piezoelements.

Phys. KN Kilchevska engaged spivudariv theory of elastic bodies, variation theory of bending plates, stability of elastic shells, etc.

The subject of study Assoc. RI Miloshynoyi is the theory of random processes, the study of limit theorems for controlled stochastic processes and queuing theory.

Main area Assoc. OA Myrontsya - algebraic theory of topological groups, the study of topological groups on the properties of systems of closed subgroups.

Scientific Research Assoc. A. Mkhitaryan related section of continuum mechanics, namely elektrohazodynamichnymy trends. Obtained his results have been used in flight experiments on the flight-test station ASTC "Antonov" (Kyiv).

Phys. ZI Naholkina engaged in research on the existence and study properties of solutions of nonlinear stochastic differential equations in functional spaces, explores the stability of differential equations in Hilbert space and creates mathematical models of conjugated problems in convective heat flow unisothermal surfaces.

Phys GK Novikova has been studying the conditions of approximation of periodic functions by linear summation methods of Fourier series based on the theory of operators in Hilbert space.

Phys. NN Panasyuk explores the transient diffraction of acoustic and elastic waves in solids and elastic membranes. It also deals with mathematical modeling prediction distribution of technogenic pollution.

Analytical method of solution of continuum mechanics dedicated research assistant professor. A. Puchkov.

Phys. FG Selezneva is researching the boundary and initial value problems for differential equations posed in the Petrovskii.

Phys. AP Trofymchuk explores different aspects and modification of numerical-analytical method Samoilenko, different types of equations with delay and different models of population dynamics.

The writings Assoc. MI Chernyeya found beyond generalized convexity some special classes of univalent functions.

Research interests KF district. A. Grigorova concentrated in the theory of estimation of states and parameters of the systems described by differential and difference equations.

Scientific Search KF district. V. Mogileva related to problems of modern algebra. She examines the hereditary and napivspadkovi napivdystrybutyvni ring, and conducts research on the qualitative theory of differential and difference equations.

Research Room things. A. Klimenko associated with the development of algorithms for precision control the orientation of spacecraft.

Research Interests century. Off. VM Vladimirov apply to use the second method of Lyapunov in the theory of integral sets of various classes of differential equations.

Art. Off. VA Goncharenko explores the question of stability of differential equations and uses the results to the problems of mechanics.

Research ass. EV Masalitinoyi devoted one dimensional and multidimensional integral inequalities for discontinuous functions and their application in the study of the practical stability of solutions of systems of differential equations with pulse perturbation theory and hyperbolic equations.

Ass. SY Tseshkovsky explores the theory of catastrophes and algebraic-topological properties of manifolds and bundles.

**Professor Dobrovolsky VK**